GATE EE 2016 Set 2 — Question 14
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Engineering Mathematics → Differential Equations → First-Order Equations
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Question
Consider a causal LTI system characterized by differential equation . The response of the system to the input , where denotes the unit step function, is
Correct answer
(D) 54e^(-(t)/(6)) u(t) - 54e^(-(t)/(3)) u(t)
Solution
1.The differential equation is . Taking the Laplace Transform (assuming zero initial conditions for a causal LTI system):
.2.The input is , so .
3.The output in the s-domain is .
4.Using partial fraction expansion: .
..
5.Thus, .
6.Taking the inverse Laplace Transform: .
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